What drought tolerant plants can handle wet winters?

I have some plants that I need help placing in my flower beds. I have a few lavenders, rosemary, a few different sages, oregano, thyme, creeping phlox, and some short sedums.

I have two beds to choose from- one stays dry year round (it's under an overhang). I can water once a month or so. The other gets rain on the front, and the back foot or so stays dry. (It rains a lot here in fall, winter, and spring. It's dry all through the summer). Both beds are VERY well draining soil.

Which plants will be ok in the wet part of the one bed? Which plants might prefer to stay mostly dry, with an occasional watering, in the other bed? They are both smallish beds, so I will need both to fit all my plants in!

I think the answer is quite straight forward for these type of plants, they need to go into the bed that gives you the best light, the best draining soil and over hanging tree's are not really the type of place that any herbs would sit happy in.

Maybe the front of a border where there is more light / sun could dry out faster IF the rain became a problem, but MOST herbs are originally from places in Europe or similar types of environment and for best results you would have to do your best to try mimic these type of growing conditions, also most are Annuals which die off end of season and you restart seeds the following spring early on before the hot weather arrives.
Hope this help a little but maybe others who live in your area will be of more help, the only thing is, replication the conditions you mention which might not apply to there planting area or vice-versa.

Good luck anyway.
Best Regards. WeeNel.

lavenders, perennial, full sun, good drainage, not great in soggy conditions.
rosemary, perennial, full sun, good drainage, not great in soggy conditions.
a few different sages, Sages run the gamut from tropical, moist, even bog conditions (Salvia uglinosa) to dry conditions. If yours are Salvia officinalis and color variations, then they are perennial, full sun, good drainage, not great in soggy conditions.
oregano, perennial, full sun, good drainage, not great in soggy conditions.
thyme, perennial, full sun, good drainage, not great in soggy conditions.
creeping phlox, perennial, full sun, good drainage, not great in soggy conditions, but more tolerant of water than the other plants in this list.
some short sedums, most are perennial, full sun, good drainage, not great in soggy conditions. A few do not mind a bit more water, but must have good drainage.

What I would do:
Prepare the soil so that there is the best drainage possible. Perhaps build up a raised bed, if this will work.
Plant the plants in the order of their preference for sun.
Hope that the winter rains do not drown them.
Set up an irrigation system so that you can water the plants in the summer, and under the eaves in the winter, in those spots that stay too dry. A drip system will deliver the water right to the roots where it can be best utilized.

Other herb types of plants that might handle a bit more water:
Lemon Balm (perennial)
Sweet Basil and most of its varieties (summer annual)
Parsley (treated as an annual)
Lemon Grass (perennial)
There are probably a lot more...