I believe that the EU is bureaucratic and often wasteful. MEP salaries are very high. With input from 28 countries, decision making can be slow. The rise of nationalist governments and their input concerns me. The common market is protectionist. The balance of power within the EU is not equal, and some countries benefit more than others.
I also believe that its existence supports peace in Europe, improves living standards, animal welfare standards and environmental standards through regulation, and think that freedom of movement and a common market are beneficial to the UK and other EU member states. EU funding is much better targeted at areas that will benefit from it than much internal funding is (e.g. much higher levels of funding to the SW, Wales, Midlands from the EU vs UK which is generally weighted towards London). We are net 'winners' on scientific and medical research funding as it's an area in which the UK excels.
I voted Remain. Others who believe the same as me might have voted Leave.
So, I've given reasons for voting in each direction. But I also don't really think that most people were swayed by reason (including me). The vote was generally instinctive and reflects a person's identity and emotional state and how they view their national and international identity. I am someone who supports open borders and the creation of global communities. Citizenship is, for most people, an accident of birth, and so I don't understand nationalism. If someone wants to come and live in the UK I support it completely because it means they think the UK is a good place to live. I support high taxes and a welfare state. I want different people and countries to work together to improve life for everyone, no matter who they are, where they were born or where they choose to live.
I have a friend who voted Leave. He has, through circumstance, had to rely on himself for everything from childhood. He is a lovely man who helps others without question, but who does not believe that others would ever do the same for him. His self-sufficiency reflects his belief that the UK can 'go it alone'. I don't believe he's xenophobic or racist or stupid. It's just that there is nothing that will change his mind because it's so much part of his identity as an isolationist.
(Also, you can be xenophobic, racist and stupid and vote in either direction. You don't have to be white or born British to have voted Leave; I know multiple immigrants who voted that way because they believed it might mean more spaces would be opened up for others from non-EU countries to immigrate, for example, or reduce the costs for non-EU immigrants to live or work here.)
OP, I hope that you and your DH can come to an understanding. His vote sounds instinctive - is he someone who is very self sufficient like my friend, someone who is dissatisfied with the status quo, someone who feels disenfranchised or someone who has a strong nationalist identity? Maybe this will give you the opportunity to connect more deeply with other issues or personality traits that you were both unaware before this.
Good luck to you both through this all.