It's hard. Very hard.
I remember being very much like that and finding wrong everything that DH did to look after my first. In hindsight, I think the father also needs to try it his way. There's not one single solution and your baby might settle with you one way and with him another ONCE she gets used to it. In the same way that they do with nannies, childminders and nurseries. I didn't give my DH a chance to look after my first, I was always there saying what was wrong, do it as I do, why are you doing this, she doesn't like that... Not nice and to be honest, unnecessary. I know it was an instinctive reaction but you might be making difficult that they bond. And they need to bond. And your child might cry for a bit too long, but your DH is trying and he will get the knack of it if you just let him. Or find his own way. I'd write together a list of things that you know work when your baby cries. Put it on the wall. Let him go to it and read when he's trying, instead of you saying do this for that. Learn to identify the different cries. I had no clue with my first but amazingly both my DH and I could easily identify my second's cries. Write common cues and solutions, such as rubbing eyes or ear means tiredness, wetting lips or showing tip of tongue means hungry, "cough" cry (eh eh eeeeeh) usually is hungry, etc. There are a few cries that apparently are common to all children. Get it all down. And visible. Let him fail, let him reach the paper, let him ask you if needed be, step back a little. I know it took me a good while to let go, to let him try, but it actually worked. My children would go to sleep in different ways with me or him, not massively different, but small differences that I had been stubbornly saying "s/he won't do that". They also were winded differently and worked anyway. Make two lists if necessary, one for feeding / reflux, one for general advice. Times for feeds too. It's hard and many of us tend to go into overprotective mode and want to be there and micromanage everything... But it doesn't help anyone: your child will benefit from different approaches as long as there's a routine, your DH will bond and feel involved in bringing up his children (they already feel usually quite left out), you will be able to relax later on when / if you need to leave your baby with DH for any reason (hairdresser, hobby, go appointment, meeting people, returning to work, whatever), as you will have realised that it's ok , he looks after baby and they are both happy. I know at the moment is about reflux / colic but at the same time that's something for which there's not a single solution, my first had it and it was horrible. But she would cry no matter what sometimes, my way, his way, it didn't matter. Don't make him feel guilty because maybe, just maybe, if he had done what you said he might have had the same result. All I remember from those days was: keep baby straight up fir 20 min after a feed (I bought a carrier for that), try to feed baby as upright as it can be whilst still comfortable / safe for the head, warm milk instead of cold (if not breastfeeding), "bicycle" legs slowly and bring their knees to the tummy together to encourage passing wind, keep tummies warm, smaller feeds (an issue with evening cluster feeding, though) and a change of milk if it didn't work. We tried the usual stuff like infacol, but it only worked to prevent wind and only once established. Gripe water was too much for my little one. It just disappeared one day but between 2 and 5 months old, it made our life quite difficult!