Since ssh is a layer4 tunnel if you don’t run a proxy on your home box, you’ll need a new network connection for each service, if you are fine with that, I would set it up only on the VPS. This means if the tunnel goes down, you should at least get 502 error rather than a timeout or connection refused.
Alternatively you could forward 80, 443 to a proxy service on the home server. That would require two ports for the ssh.
You can drop it to a single ssh connection by having a proxy on both and just have the VPS proxy Http and https to the same port on the home server.