I have a bit of a different perspective.
First, this is a serious problem since he is to be the main instructor. It should not be brushed aside.
However, I would encourage both of you to not make this an "all or nothing" debate. So, he has a poor math background and is nervous about teaching it. I actually have the same exact weakness!
In fact, math was my #1 all-time worry about homeschooling. I went to Christian school, and the math program was fine (I think), but I seriously struggled all the way through. Pair that with a horrendous algebra teacher in high school, and I am very, very dismal in math. I remember crying over addition flash cards in first grade and it never got any better. I actually think I have a learning problem in this area. My brain just does NOT seem to process numbers well at all.
What we did long ago, when we were deciding to homeschool, was to take one year and go around a (very large) curriculum hall and look at nothing but math programs. My mathy husband was to examine them technically, and my job was to figure out if I could teach the one he thought was best. This was back when the ONLY program with videos was Math-U-See. We ended up going with a scripted program (Professor B Math--back then was only books that I read a script out of, but now has CDs and an online option). We chose it because I understood things about math I had never understood before from the interactions at his booth, and because it was scripted. Every day, I would read the script. If my children didn't understand it, I read it again. If they still didn't understand it, Dad helped them when we got home. We did this for YEARS. Neither of my children "inherited" my math problem. Both of them are at least competent (although my daughter dislikes it).
Here's the point of my story: I knew my weakness and was determined not to pass it on. I made sure I got extra help in that subject. Your husband can do the same. So many helps, video programs, and online programs are available. If you wanted, you could even enroll them in something that did the grading for him.
It's pointless to try to determine whether a monolithic concept like "homeschooling" is responsible for your husband's weak areas. Many who went to traditional schools have weak areas for some reason. I do not consider my K-8 school responsible for my math weakness.
Phonics is a little trickier, but again, helps are available. And you might be able to help in the evenings with that.
The key thing is to recognize weakness, compensate, and do your best to ensure that weakness is not passed on. That can be done, one subject at a time, without throwing out the whole "homeschooling" baby with the "math" bathwater.