I just went through the process of discernment for the diaconate (not selected) after feeling and hearing the call again (after ignoring it for 14 years). Each diocese is a bit different, but the Church does have a set program. Our diocese could only accept 40 or so of the 120 who applied for discernment.
The Bishop assigns the deacon to whatever duties he wishes, which may or may not be to a parish. It can be very time consuming, but from the get-go, the first thing the diaconate leaders told us is that the priorities are family, work, church when it comes to duties. That said, many wives also said they had to rein in their husbands; being passionate takes over sometimes. Some wives were very involved with their deacon husbands, others were not, and other were involved in other church ministries.
I know of one deacon from our parish who had a small child when he entered the program, and had at least one or two more after. It is very much a personal decision between husband and wife in answering God’s call. In the end, if the wife does not consent (and your husband may not ever know if you do not, unless you tell him) via a signed letter, the man is not accepted as a deacon.
Your comment on the church wanting a long history of volunteer work is probably true; we alo have four kids, though two are older. We have done what we can within the church, usually teaching RE, but not a long, deep involvment. Also, part of the discernment process is filling out some personality tests/compatabilty tests, kind of like what is used during engaged encounter. Though we were told that these would not be used to rule anyone out, I didn’t wholly believe it. They have to use something subjective. But if it shows you and your husband have areas of disagreement you need to communicate on, and we do in several areas, I would think that the decision-makers would be looking at those areas being resolved first, before a man becoming a deacon.
Continue to pray for your husband; it is a tough decision. For me, it was the first time in 14 years I felt God again, and it is utterly humbling to think God wants you in that capacity. That said, it was tougher than I thought when I was not selected (diaconate leaders discern who they will accept into the program; it is not a sure thing because someone thinks they are called). It may well be your husband is called, but in God’s time - easier to say than to accept!
God bless - I’ll keep you in my prayers.