Sounds like you two are primed for an adventure in NVC (Non-Violent Communication). This is a fabulous process that my husb and I use to get to the bottom of our "issues," and every single close relationship develops issues. You can google those terms for more complete explanations, tips, examples, books and videos, but here's one application of the basic process that might fit your situation:
1. Listen respectfully, with your heart, to a criticism or angry comment from your DH, and observe/summarize what you believe he said. Use non-judgemental language. "I hear you worrying that I don't listen carefully when you express your own opinions about X. Am I "getting" you?" Be prepared to adjust your statement until you are saying something you can both agree upon.
That step alone could surprise you both: he might feel the unexpected satisfaction of your attentive listening. And his response toward you may suddenly be less insistent that you don't listen, because you just did.
2. Make an observation, and report your genuine feelings about it. Make sure you state feelings ("I feel mad, sad, glad when…") and not concepts (I feel you don't respect me / listen to me / care about me, when…"). Feelings just are, and are hard to argue with. Concepts are often a point of argument. (You will express the concepts in the next step, stated as needs. First, get real about your feelings. Example: "I have noticed that when I express a strong preference that's different from yours, you don't let me know that you heard my preference; you just tell me I didn't listen to you. When I hear that, I feel frustrated, and confused.")
3. Tell what needs of yours are going unmet, some of which might be: "You know, sweetheart, just like you, I need to be heard. Just like you, I have ideas that seem really good. I need us to find a way to support and respect the well-intentioned thoughts we do have. I want to learn how to avoid those arguments that really get us nowhere. I want to find a way to treat each other with warmth and caring, even when we disagree.
4. Make a request that is within your husband's reach. This might include: "I hope you will help me figure out how we can achieve that. Are you as exhausted as I am by those big arguments? I need your help in finding some common ground to build on. Would you be willing to learn and use a new set of ground rules when we feel an argument coming on?"
Obviously, I don't know the details well enough to give you a perfect script, which will, at best, come from what is best and strongest in you and arise from your particular conversation. And even if your husband thinks its not worth his while to use this new system, you can use it yourself to good effect. He may eventually pick up what is valuable and productive and start using the four steps himself. My husb and I use variations on this process almost automatically now, and almost all arguments stay small and get resolved peacefully. Good luck.