Depending on your airlines plan it can work out very well to take the Tricare Prime and the company plan for yourself. The company plan becomes primary and the Tricare becomes secondary.

The effect is that the Company plan pays first. The remaining is paid by the Tricare. Reducing your out of pocket to zero.
This works well if the company plan is low cost. For the company I work for the Health plan for an Individual is greatly reduced from the health plan for with dependents. So, if the cost for having you on your wife's plan is more than the cost for your airline plan I would take your airlines plan (assuming the plans are similar).
Medical,dental,vision plans vary between the airlines and I would wait until I was somewhere and then ask people in a similar situation to you as to what works best for them.

Just my 2cents.