One of my insurances has approved; should I wait for the other?

I don't know if I'm being 'greedy', but here's the question. I have primary insurance through my job and secondary through my husband. I've just found out my husband's insurance (secondary) will approve. My primary claims they still haven't even gotten the paperwork! So, should I go ahead and schedule my surgery now, be thankful at least one approves, or should I delay and wait for my primary? I feel I am being greedy and should be happy for the 80% coverage, and not hold out for 100% coverage, but then again, that 20% does add up. How did others of you in this situation handle this situation?

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