>>>some people have said just find out if the convictions have been spent
The USA doesn't recognise the UK's Rehabilitation of Offenders Act (and has no similar legislation); therefore convictions are NEVER regarded as spent when applying for a visa.
The USA's Immigration and Nationality Act places an
automatic bar upon anyone entering their country if they've been convicted of of an offence involving 'moral turpitude'. (It's possible for such people to seek a 'waiver of permanent ineligibility' but it's a long-winded process, taking many months).
Drug offences normally come under the heading of 'moral turpitude' but the automatic bar on entering the USA has an exemption for people who committed a SINGLE offence of moral turpitude whilst still a minor.
Most offences of violence DON'T fall under the heading of 'moral turpitude'. However 'intent to kill or 'intent to commit serious bodily harm' moves an assault offence into the 'moral turpitude' category. It would be for the US authorities to try to match up UK legislation with their own but it seems likely that a 'Section 20 (GBH) offence wouldn't count as 'moral turpitude' but a 'Section 18' (GBH with intent) offence would do so.
If your husband's offences are not regarded as 'moral turpitude' then the US Embassy might well decide to grant him a visa (because of the length of time that has passed since his last conviction). If they do fall into 'moral turpitude' then the US Embassy MUST (in the first instance) refuse to issue a visa. (They have no choice; they're bound by the terms of their Immigration and Nationality Act). They could then refer the application to Washington to see if a 'waiver of permanent ineligibility' could be issued.
Seeking to travel on an ESTA would seem to be very unwise. While the UK doesn't automatically share information about criminal convictions with the USA, a great deal of data seems to be passed on under the guise of 'anti-terrorism' (which lets the UK get around EU privacy laws). Your husband needs to apply for a visa AS SOON AS POSSIBLE. If a waiver of permanent ineligibility needs to be sought there's hardly any time left. (As stated above, the process takes MONTHS).
See here for the current waiting times for visas (taking particular note of the section on 'administrative processing'):
http://travel.state.gov/visa/temp/wait/wait_4788.html?post=London&x=49&y=20
By changing the location to Belfast you'll see that the 'basic' waiting times there are shorter (but that 'administrative processing' takes just as long).
See also here, which states that a wait of AT LEAST SIX MONTHS is likely:
http://london.usembassy.gov/add_crime.html
Your best option at present would seem to be to speak to the travel company to see if the holiday can be postponed by several months, and for your husband to begin the visa application process NOW.
Chris