...unless you're a serious snuggler (which, according to your post, you're not). Weight (both yours and hers) is going to seek the lowest point in the hammock, which means that you're going to be pressed against each other all night long. Sleep may be possible, but I'm pretty sure that it won't be particularly comfortable.
Clark makes a couple of models that are true-two person hammocks (not just a single-person hammock marked as "double" to indicate that it's bigger than their stock model); their Vertex and Flex 180 models. Unfortunately, neither of those is even close to your target weight of 24 oz (the Flex 180 comes in at 70 oz, the Vertex at 90 oz).
There have been several different attempts over on Hammock Forums to use hiking poles as spreader bars for two hammocks hung from two trees (and there's the always-popular three-tree hang). Starting there may yield some help; I think two smaller hammocks could come in under your weight limit, even with suspension.
Hope it helps!