It would depend. $20,000 is 2/3 of my current salary, and likely any future job I get will settle at or around $30,000 as that is what the pay tends to be for what I do.
To take a $20,000 pay cut for me would obviously be devastating.
I assume that for your DH $20,000 is not such a huge chunk of what he is used to making. However , if it is, you may want to wait.
I would ask yourselves a few questions :
Can you get by on what his new salary will be without having to make signifigant lifestyle changes?
How is the job market in his field/area?
Does this job have room for advancement?
Would he possibly be at or around his usual pay within 3 years?
Would benefits come after a certain amount of time there?
Money is not everything. Would he be happier at this job than at a higher paying job that required more time, travel etc. ?(that's a big thing for me....I could be making a lot more if I was willing to devote more time to a job but I prefer to have set hours and weekends free).
Being employed, IMO, is better than being unemployed and a pay cut is better than nothing. He could always take this and then keep looking/doing phone interviews until something better comes up. The job market is improving, (well, I can only speak for my area). My company alone just hired 6 new employees for the first time in a year and a half.
My only concern about this job would be the lack of benefits / health insurance. I suppose that depends on your personal needs, but I have medical conditions that require ongoing care. If you are paying for health insurance yourselves, you could maybe continue to do so.
Good luck to you in whatever you decide.