So let's see, do you mean a conceptual backstory for your gaming models, or a meaty idea for the army fiction stories you want to write?
Or both?
Anyway... I immediately think of two basic situations.
1. They are cooperating well
2. They aren't.
Since Astartes are (in the fluff) soooperrr huuuumaaan badasses, enhanced with amazing bio technobabble processes, and armed with kick-donkey war stuffs, they are not merely Army Special Forces, or even like any nation's current Marines, excellent though those be. ...so sometimes in stories they have a nine- foot titanium stick up their posteriors. But then, some chapters don't.
Are the Astartes there to rescue the Guard? To lend a tactical punch to the
IG mission? To be supported by the Guard? To accomplish a related but separate mission from what the Guard is doing? To conduct a totally unrelated mission, but they are coordinating shared resources or operating from the same base for strategic reasons? Does the Guard even know why the Marines are there? Or is that classified? Have the Marines arrived to take over the operation? Because the Guard stumbled onto a classified bit of info or situation?
More ideas flashing through my head too fast to record them.
Anyway, if this is background for your actual tabletop army, then in practicality, they must be working OK together. Probably for the obvious reason: the
IG are stationed here or nearby, and are naturally called on to fight whoever your tabletop opponent is. They have manpower and they have The Guns. Your Marines are also stationed nearby and feel a tactical or moral obligation to assist with this threat, using their Armored Angel of the Emperor training/enhancement/mystique.
But I guess yeah if you think of your gaming sessions as episodes of a dramatic action TV series featuring the interaction of
IG and Marines, then the exact reason they work together each time might change with the battle scenario. And the specific units you bring to the table each time might change. You get to decide the dramatic interpersonal "off-table" interactions that enrich your War game on-table.
But I'm guessing you won't fail to support yourself because of political tension in a dramatic season-climax episode!