What field is he in? A professional school (law, medicine, etc.), or an academic field?
The rule for an academic field is never to go into any debt to go to grad school. A good grad school will cover their students' costs, through tuition wavers, teaching appointments, etc. Some grad schools (e.g. Harvard) will offer some places to people they don't cover. This is only very rarely a good idea. If the school is someplace less than Harvard, it's always a bad idea. So if your husband is going to grad school for an academic field, he should not be paying. Things have gotten even worse than usual in recent years, as academic jobs have dried up. So some poor souls are emerging with $100K+ in debt and no job prospects.
If it's a professional school, it may be worth it, since debt is often the only way to get into certain professions. I would be sure that he has good job prospects and that he loves his field, though. There are a number of unemployed and/or miserable lawyers out there.
If any of those scenarios applies, then the answer to "How much to keep in cash" is "All of it."