this may be simplistic - but it is how multiple insurers operate - which they would take into account any other forms of reimbursement or grant if paid in advance......
In my case, mom's insurance paid out the max to the plan AFTER any deductibles. dad's would come in and following the deductible if any it would then pay out to the max.
the grants to an insurer would be the equiv. to paying the deductible portion and what was left over would then cover the insurer cost to the amount of the grant to cover its expense to covering the cost of the service - anything not covered by the grant would then be jusy a regular expense cost to the insurer as if there was no grant in the first place. As you are aware, the insurers will only cover up to the max allowed by your particular plan.
if the above made sense, in our past we had a child who required surgery, then ortho type bracing to allow the child's legs to heal and grow even, straight and strong. What we did to ease our confusion was to identify both insurers of each other's existing plan and coverages by sending the written plan parameters to both insurers so they knew up front what the scoop was -- then we all got together so everyone was "on the same page". So in the end the second insurer allowed us the credit for any deductible we covered on the first plan and the second plan took over and covered the rest of each month's billing (we went on a monthly payment plan for two years to cover the expenses as the treatment progressed as it allowed us the best tax credit consideration for our yearly employment taxes - it would have been advantageous to get it all paid in one year to max that credit but we just couldn't afford it all in one year.
If I got this right as far as your particular circumstance (you did lack detail) then the most important step is to get all the parties the full plan details and the insurers who handle these type of two, three or more participating parties to cover these big expenses (who is the first to pay, second, third etc.)...... now that I think of it, we were lucky in that the two insurers ended up assuming 100% of the expense and we paid NIL as far as our deductible...
hope that helped!!