Thanks!

Put up a physical barrier like a nice high stone wall or very strong fence with many rails instead of pickets. Then chainsaw or cut back with a weed-whacking steel blade any thing coming over or through if chemicals are not an option. This will give a more manicured appearance. JMHO Aloha

First cut back and mow an area about two eight feet beyond your property line. I might even get out the roundup pump sprayer on it afterwards.

Second. This fall start planning your living privacy screen. I like a bush and tree combination. More different species the more interesting it is and the less likely the whole thing can be killed at once by the wettest fall ever, the invisible arborvitae gyspy ash borer, or whatever. Plant these a few feet on your side of the property line. Anything that gets taller than eight feet will do. I think evergreens are not necessary but would include some.

Third, mow every so often on the other side of the line, not the whole thing, just one or two mower widths. Every so often you may have to take the roundup to grape vine or the like.

Good luck

If the neighbor's property is uphill, honeysuckle seeds will continue to reach your property. [I don't know if they're also spread by birds, though I suspect not, since I never find seedlings under the shade trees in my front yard.]

Another possibility is to have someone till your side of the property and hope there's no rain for a while. That did wonders for the honeysuckle situation in part of my pasture (I actually had it plowed for planting vegetables, but it killed the remaining honeysuckle I hadn't eradicated in that area).

http://www.nps.gov/plants/alien/fact/loja1.htm
http://www.imapinvasives.org/GIST/ESA/esapages/lonijapo.html

Both sites also have information about fighting other particular nasties.