It really is a phase and not personal. You are the stay-at-home parent, and your son has a closer bond to you at this time in his life. This will pass as he gets older, believe me! As he becomes older and there is more going on in his life, he'll discover that dad is an important part of his world, as well. For now, encourage your husband to enjoy being with his son. When you are alone with your son, perhaps while dad is at work, bring daddy into your son's life more. When my sons were small, we'd call daddy at work, and I talked about daddy a lot during the day. We did a lot of, "When daddy comes home, we'll be so happy!" And we'd plan special welcome home activities, like little cheers and practice big hugs and kisses for dad. Build dad up while he is at work, and your son will eventually develop an anticipation for dad. Those will be the positives in your husband's life.
As for bathing and bedtime, my sons did the same, but frankly, after being with them all day and being totally exhausted by that point in the day, I didn't care too much. It sounds harsh, but I was just so tired. Ugh. I've never felt as tired as I did when my sons were little, not even when I've backpacked 20 miles in a single day! LOL. This is a brief time in your son's life. Before very long, he'll be bathing himself and won't want either one of you in the bathroom with him. Build up anticipation for bath/bedtime with daddy, perhaps buy a special book that only daddy will read at bedtime, or a special toy that only daddy can use at bathtime. Over time, there will be special times when your son will prefer dad and not mom. So, encourage the relationship between the two of them.
Just as a point of perspective... my sons are 20 and 18, and my husband shook his head just the other day and smiled. My sons and I are very close. They are close to dad, too, but in a different way. When they want to talk about something, it seems that they come to me more often. My oldest is home from college and is about to leave for his summer job. He wanted to have a general gab-fest with me, so he made me breakfast this past Sunday, and we sat at the dining room table for about 2 hours just talking. My husband walked through the room at one point and just smiled, commenting... "I guess no one thought to make me breakfast!" You see, the breakfast routine is something that is special that developed over the years between my son and me since my husband usually leaves for work. My son happily crowed, "Don't worry, Dad! I left you some bagels and there's coffee, too. I was hoping we could play tennis later, so you better fuel up." That made my husband very happy. I wouldn't be caught dead on a tennis court! That's something dad does with his son.
My point is, you will be a family for the rest of your lives, and you are just at the very beginning of the adventure. Your relationships together, the dynamics will change many times, but if you love each other and live well together, your son and husband will eventually have their own special bond.