Shorter answer is yes.
(my wife and I are in the process of doing the same thing)
Assuming you are on the spousal route, you can apply for UK citizenship as soon as you have ILR (as long as you meet the 3 year residency requirement). The citizenship application takes around 6 months to process, then you have 3 months to attend a citizenship ceremony, then you can get a UK passport. There are other threads on here describing this process.
I am a UKC. I applied for my 'green card'. Steps are outlined here
https://travel.state.gov/content/travel/en/us-visas/immigrate/the-immigrant-visa-process/step-1-submit-a-petition.html [nofollow] First step was the i-130 petition. This took FOREVER to be processed (almost 1.5 years). Then you pay fees, complete the actual visa application (DS-260) and submit a bunch of forms to the National Visa Center. I am currently waiting to hear back from the NVC having submitted all relevant forms. I thought this step would take around 6 months, but I am still waiting... (with USC wife getting more frustrated by the day)
It is difficult to match timings, as there is no expedited US service, so it just takes as long as it takes (My wife wishes I submitted everything far earlier on). Probably best to
apply for US visa as soon as you can. Even when your husband has the 'green card' he just has to go to the US to activate it and doesn't have to stay there. He can come back to the UK for at least a year (useful if you are still waiting for UK citizenship).
