What you're thinking of is called DAV, also called "web folders".  Unfortunately I don't think it can be made to play nice with a normal permissions structure (like a home directory) as DAV requires folders owned by Apache (for security purposes) and mode 700 IIRC.  It's a little complicated to figure out the first time if you're not familiar with running HTTPS, but once it's set up it's really easy.  I used it for quite a while to synchronize bookmarks between my home and work systems (now I use Weave).

Good luck.
J.



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"He that would make his own liberty secure must guard even his enemy from oppression; for if he violates this duty he establishes a precedent that will reach to himself." -- Thomas Paine