There are ways to successfully control this plant. The subject has been discussed numerous times on Gardenweb over the past few years. The link below is a decent summary of many methods compiled by the Nature Conservancy. As for herbicide use for this, it is important that certain things are done for this to work well. For example, it usually takes the addition of a surfactant to the mix, and the use of herbicide label rates that are higher than would be used for easier to control weeds. You can get very good control though.

Here is a link that might be useful: TNC link

Don't give up, there is no plant/weed tougher than a determined gardener :)

Here is a link that might be useful: Everything you'd want to know about ivy removal

PERSISTENCE.

Trimming it back, spraying extra-strong weed killer with a dash of dishwashing soap on the new growth, and repeating this process frequently helped me get some out of control ivy to a manageable level. I hated using that much chemical, but the previous owner would've let it take over the house she hadn't sold it to me first!

Good luck.

Apply Roundup (with a dash of dish soap) once a week for 3 or 4 weeks. Then pull the plants from the roots.

Some of the plants will re-emerge. Repeat the process on the ones that do.