Since you are both still studying, the easiest way to get to the UK is to try for a student visa - maybe you could go to grad school in the UK (your husband could join you as a student dependent)?
Student visas are not that difficult to get compared to work visas, but do have a couple of drawbacks - one is that international tuition fees are very expensive (you'd be looking at about $20,000 for a one-year degree) and you'd have to prove you can support yourself (fees and living costs) without having to work at all - either with your own funds or by getting a student loan from the US and two, time spent on a student visa does not count towards citizenship and you are required to leave the UK at the end of the degree programme.
Another temporary option is the
BUNAC scheme, whereby you can live and work in the UK for a maximum of 6 months after you have graduated (to qualify you have to currently be a student or start the scheme within 6 months of graduating) - it's by no means permanent (you have to return to the US after the 6 months are up) but it's a great scheme to take part in, it gives you an idea of life in the UK and it gives you some UK work experience.
A third option to spend some time in the UK temporarily is to try and take part in a study abroad scheme through your university (obviously this depends on how far through your degree you are) - it's a fairly simple process to be able to study at a UK university for a semester or an academic year as part of your degree programme. I did the same thing - I'm British and spent a year studying in the US as an undergraduate. I've now gone back to that same US university as a PhD student and will be able to live here for at least 4 years on a student visa.
In terms of work permit visas, I'm not sure if you'd be able to get one or not (I don't know too much about job availability in your degree areas) - they can be very difficult to obtain as the UK company has to prove that no one in the UK or the European Union (that's 27 countries in total) is suitable for the job before they can give you a job offer and apply for a work permit. So usually work permits are granted to those who are highly/specially-skilled (e.g. academic professors who are part of a small worldwide community in their research area) or those trained in professions that are in demand (in shortage) in the UK (e.g. scientists, nurses, teachers, doctors etc.).