Hi T.,
If your son has always behaved this way, then it is clearly not a phase! Are you saying that from the time your son was born, he has rejected your husband's efforts at taking care of him anytime that you are around?
Maybe I am old school in terms of my parenting, but why is your husband asking your son if he can do those things for him? I believe in the parents being in control. No asking if it's okay. When it's bathtime or bedtime, the parent who will be taking care of those duties can simply say "Okay <son's name>, time to have your bath" No room for negotiation. If he says "I want mommy!", you'll need to say that you are busy with other things. I believe it's okay to tell kids that you aren't going to parent 24/7 when there's someone else available to meet their needs. But if you've always given in to your son's demands, this will be hard habit to break and there will likely be tantrums. What you might want to do is start with things that are optional such as going to the park, playing a game, reading a story - your husband should offer to do these activities with your son. Not "Who do you want to take you out to play, Mommy or Daddy?" but simply have hubby ask "Do you want to go out to play/read story/play a game?" and having mommy instead simply isnt' an option. Your son doesn't need to consent to the playing, story or game, but if he wants to do these things, it's only with daddy, mommy is just not available.
However, since your son seems to have a strong want for time with mommy, my suggestion is also that when you get home from work, errands or whatever else, spend some time with him as soon as you get home. But let him know what the limits are! Tell him you'll read two stories and play one game of Candyland, but then you're moving on to do other things, or set the timer, let him know you have 30 minutes to devote to him right now and when the timer goes off, he needs to entertain himself and anything he needs, he has to ask dad for.
Good luck!
M.