If I marry someone in a different service after having already received my orders, am I able to change my orders to get a joint assignment?

Each service has a married couples program for couples WITHIN their respective service (the Married Army Couples Program, for example). Sadly, there is no overarching joint program between all the different branches.
The level of logistical complexity in making that a reality somewhat precludes it's existence, unfortunately.

You need to get married and enroll. Be prepared for bad news. There is a developed topic page for this topic here on RP: https://www.rallypoint.com/topics/marriage/about

It has resources. Understand you are already an inbound to that installation, if not a specific BDE. Not sure what LT Asssignments branch can do. You need to do some leg work to figure out assignments that will work for both of you. You may need to suck down that assignment to Stewart while your spouse to be gets their initial assignment with the aim of the follow on being Joint domicile. Especially as you are not yet married. There is no assignment consideration for either of you without being married.

Hard reality here is being married as officers to another branch will be very difficult for you to both be active duty and reside close to each other. You getting married and him having no orders really wont change your orders because he does not have orders. Kinda hard to change your orders to a location that he does not have yet. Is that the question you were really trying to ask?

Joint domicile is the program for army and other branches who are married to enroll in once married. When your both enrolled it will show up on your SRB your married to another service member and are enrolled into the program. I am also married to a marine and i am currently in the army. Your most likely stuck with those orders unless you try talking to S1 and seeing what can be done for your situation ma”am. You may have to look at the reality that you may not get a chance to be stationed together till next PCS unfortunately. There are not many stations close for marine corps and army unfortunately and it is difficult to be stationed together. Hawaii is a good station for your type of dual military marriage due to it has all the branches on island just for future ideas of a chance of being stationed together. Best of luck!

More specifically:
The Married Army Couples Program (MACP) provides Soldiers the opportunity to establish a joint domicile while fulfilling the Army's mission. Service members in the following categories may apply: Regular Army (RA), USAR Active Guard Reserve (AGR) and Title 10 ANGUS AGR Soldiers married to active duty members of the RA, RCs, other active duty U.S. military Services, USAR Active Guard Reserve (AGR) and Title 10 ANGUS,

In accordance with AR 614-200 Section IV, enrollment in the MACP does not guarantee reassignment together but does ensure that both Soldiers will be automatically considered for future joint-domicile assignments. Soldiers should submit a DA Form 4187 requesting enrollment in the MACP, with a copy of their marriage certificate to their Bde S-1/BCT or MPD who will take the necessary action to update to the Total Army Personnel Data Base (TAPDB).

Soldiers married to a member of another branch of the U.S. Military (Air Force, Navy, etc.) are not eligible to enroll in the MACP program for automatic joint domicile consideration. However, Soldiers may request reassignment to join their spouse by submitting a DA Form 4187 to their career branch at HRC, Fort Knox, KY. The Army's intent is to extend the courtesy of the MACP to the other services and accommodate joint domicile whenever possible, with the needs of the Army being the final determining factor.

Soldiers may also update their preference for joint deployment or separate deployment cycles via the Assignment Satisfaction key (ASK) web page. The deployment preference is used by HRC assignment managers in the reassignment process and commanders as they deem appropriate.

For inquiries related to assignments contact your branch manager. Branch manager information can be obtained at the HRC website https://www.hrc.army.mil/

For inquiries related to “policy issues only” please send an email to the appropriate POC below. In the subject line, include “MACP policy issue" as well as the Soldier's grade, full name, and last 4 of SSN. The message body should contain the full name for both spouses involved. Please note that this branch does not make assignments.

The point of contact for Enlisted Soldiers is the Enlisted Procedures and Soldier Actions Branch [login to see] or [login to see] .

It’s difficult enough to get orders to the same duty station within the same branch of service; better chance with geographical duty stations. But to add two different branches of service with hopes of getting same duty station or even geographical duty stations is a far reach.

I’ve experienced both situations, and 20-years later I only had one same duty location for 6-months before my PCS and that was with the both of us in the same branch of service. We never had even geographical duty stations while we were in different branches of service.

Most dual military couples make LOTS of career compromises which is a tough dual military career; some simply chose marriage vs military service.

Best of luck!

Possible, but unlikely/difficult. To explain, once upon a time ago, I had an XO in my unit at FT Irwin, CA. His wife was a Marine Officer. She was stationed at 29 Palms. That was the closest the military could get them.