Proper weed treatment for mixed Bermuda/Centipede grass

I have the same thing and I'm gonna try the Scott's turf builder weed n feed in the yellow bag. Says it's safe for Bermuda and centipede.

The biggest problem with having both centipede and bermuda together is fertility. Bermuda needs higher rates of fertilizer, but centipede is very sensitive to over-fertilization. Too much nitrogen can cause decline.

As far as herbicides go for the most part, if it's safe on centipede it's generally safe for bermuda but not the other way around. Bermuda is tough as hell and can usually recover from just about anything.