Treat him at the level of customer.
Like bosses, most customers also tend to be less technical as well; and at times, even if they have some background, they might want to avoid technicality.
Every communication thus needs a little more perspective and details from overall view. In a way start from a 50,000 feet view and add detail as you go down - till the point he is sufficiently happy to know. So in all this is a problem of structured communication.
This structured communication implies:
getting them to know overall elements of the system and how they work,
getting then to appreciate a general process that goes in development of such systems.
when you are stuck in some problem, you need to give them some background and how you are planning to solve them. They should also know what remains essentially straight forward but common situation and what remains essentially non-solvable problems.
In all cases, whatever you say, should make sense to them and should never sound like excuse (in the guise of technicality)
The essence is, how do you translate most of your issues and status in a layman language, there will be improved communication and learning; and when people begin to understand stuff, they tend to listen better and increase the appetite to dig more or at least trust you that you are on your way to get things right.
All that sounds like more work, but that's what you need to pay for having such a boss.