Is it possible to adopt without the natural father giving up all his rights?

It may sound silly at first, but here is my problem…
My SO would love nothing more than to be able to adopt my son Xander. My son’s natural father still has some rights to him and I don’t want to take those away. I want the natural father to stay in the picture as much as he wants. He really is not a big part of my sons life right now, and I don’t see that ever changing. There is a good chance I could be traveling a lot with my SO since he is in the military. I am moving to Guam in February to be with him and things just get very tricky when Xander is not legally or biologically his. I really want him to be able to adopt Xander because for one, I know he is going to be the prominent father figure in my sons life either way, and two if he adopts Xander, then Xander would be able to receive all his military health benefits. We have talked about him restationing in Italy I don’t even know how to get insured in a different country!! I know it all sounds confusing, and I can’t find any helpful websites so I was hoping someone could shine some light on my predicament. I think I know the answer already, but I’m hoping I am wrong.

I just don’t know what to do and I want to make the right decision.