Is it best to let my gyn do fertility testing or go straight to RE for testing?

My husband has an appointment with RE in about 2 weeks or so to discuss his infertility and options. I was wandering if I should let the RE do my testing to see if any problems on my side as well when he goes or make an appointment to let my own gyn do the fertility testing. Because I'm not sure if it will make difference as far as insurance goes if the testing is done by gyn as oppose to fertility specialist which is definitely not covered. If I go to gyn first, will the RE still do his own retesting?