Fedorable -
Sounds like an interesting concept. You've gotten some good advice here. There are a few ways forces with different capabilities have been combined in the past. The major difference between the various methods is the level at which they are combined. A few examples:
The Roman cohort legion was a combination of Roman regulars and auxiliaries (the forces provided by subject nations) in which a legion of regulars (usually between one and five thousand) would be combined with an equal number of auxiliaries under a single general. The subunits retained their own standards and formations; for the man in ranks, there would have been little difference. But putting both forces under a single commander gave the cohort legion what is called unity of command.
Especially in the twentieth century, forces have often been combined on an ad hoc basis for the duration of a fight. For the invasion of Normandy mentioned above, each nation's forces maintained its own organization, but Eisenhower acted as Supreme Allied Commander. The national boundaries shifted occasionally as the fight required it, as in the Battle of the Bulge when Ike made Bradley subordinate to Montgomery for a short time because they were on the same side of the Bulge.
Multinational forces often exchange liaisons to facilitate communication. This involves nothing more complicated than sending one or more officers to the other force's headquarters and providing them the means to communicate directly with their home headquarters. This is one of the jobs I had in Iraq (I was attached for several months as liaison to the Polish division). This is usually the simplest option, and insures a degree of cooperation between the units. Liaisons can also be exchanged between units of the same nation with different capabilies; e.g., the Marines and Army or the Army and Air Force might exchange liaisons to enhance their ability to work together.
If relations between the two nations are somewhat tense, this concept can be turned around by making the liaisons hostages. Hostages function as a sort of human shield to ensure goodwill, or at least good faith--if one of the partners fails to deliver as promised, the other can kill some or all of its hostages. This method is most effective when the hostages are persons important to their host nations.
Another method is to have them fight as combined arms forces. In the U.S. Army, this means exchanging subordinate units: an infantry company might receive a platoon of tanks, or a tank company a platoon of infantry. Battalions can exchange companies, and brigades battalions. This accomplishes unity of command, and allows units with differing capabilities to complement each other's strengths and (hopefully) mitigate each other's weaknesses.
Of course, if your nations have enough time and a charismatic enough commander, there is the intermingling option: all existing units are dissolved, and men from both nations are mixed in roughly equal numbers into new units. This is the approach often taken in fantasy stories, but I can't recall an incident where it was used successfully in history.
One of the most interesting aspects of your scenario, I think, is the potential for interpersonal conflict. How does a feudal baron act when he is placed under a colonel, especially if he perceives the colonel to be of lower birth? How does the colonel discipline him without losing his loyalty? How do serfs suddenly incorporated into a meritocratic army take the shift? How does a general act when he and his men are suddenly subordinated to a duke? Nice concept.
Hope this is helpful to you.
HN