I think questioning his ability as a father is a bit over the top... He may not completely agree with you OP even after you show him the stuff, but as long as he's not trying to force you to CIO with the baby (after all, it's the mom who does most of the responding anyway!), and won't keep trying to change it, and will support you in front of your MIL, then it's fine.
My DH is more of a proponent of CIO, but I think he's a very fit father. He just happens to be more tolerant of crying. Mothers are hardwired for their baby's cries to be irritating, for us to want to soothe them. Not that our husbands want their baby upset forever, but I just don't think that biologically a baby's cries have the same effect. I have to remember that a dad's parenting is important too, even if it's different than mine! When I finally stepped back and let my DH do his thing, yes, he does let our son cry more than I would, but when LO is really upset, DH DOES respond, he DOES try to comfort him, etc. Actually now that I think of it I'm not sure that DH really lets our son cry without responding, it's just that I tend to respond to even the little fusses & frustrations when LO isn't really upset as well, whereas DH tends to let LO fuss a bit and see if he can figure things out on his own.
Whatever. OP, you and your DH do need to have a united front in your parenting, and be able to support each other in the face of opposition from the in-laws. If you show him stuff and he's not completely on board, that doesn't mean he's not a fit parent, but I would say there are probably going to be other things in parenting that you guys will approach differently and at times you might have to support his approach instead (even if it's not what you would do). In this case, I think he should be supportive of not letting your baby CIO, even if he's not 100% convinced about it.
If my DH let my newborn cry...and wanted to let him CIO because he couldn't understand what newborns need, then I really would question his ability as a father.
I get though that some people do CIO...but it really should not be done that young.
A lot of people don't really get it, because they go by what they know from older family & friends who have done it before. New dad's don't "get" a lot about pregnancy and even having a newborn, especially if you're breastfeeding, because they really aren't going through nearly as many changes.
Like I said, just being pro-CIO isn't necessarily the issue for me, even at a young age. My DH is willing to let our son fuss more than I am. BUT both parents need to be united in what they do, regardless of what they think about it, and in this case I think her DH should follow her lead and be supportive of her tending to her LO (as my DH is with me/mine).
Also, a lot of people in general, but I've seen it more in men especially, have this attitude that "I was left to CIO, and I turned out okay, so it's a valid choice" mentality. I don't think that's good logic, when there's research saying otherwise, but you'll find this attitude in many aspects of parenting (even with contraindicating research), like formula feeding, early weaning, different discipline approaches, etc. I think it's a bit unfair to call a husband unfit when it's fairly natural to think back on the parenting experiences he knows of (his parents and possibly family/friends and how they parented) and see that in general, people turned out fine. As a family, and as a parenting unit, he should be respectful of the mom's opinion, especially as it's something she feels strongly about, but disagreement doesn't automatically make him a bad dad.