I was born and mostly raised in the US, my wife was raised here in Manila. We're worried our children will favor one culture more than the other. How do we balance their respect for both? Can anyone relate to this problem?

Maybe you and your wife can each be in charge of teaching Western and Pinoy cultures. Like, say, you can teach your kid one culture and your wife does the other. Or better yet, just teach both simultaneously if you both can.