Not really. Not only . . . but also assumes parallel subjects.
The best way to connect them, in the example you gave, is simply to drop the also:
Not only should you cook your meals, but they should be healthy.
Alternatively, you could rewrite it to make the subjects parallel:
Not only should your meals be cooked by you, but they should also be healthy.
There you're getting into the passive voice, though, which a lot of people like to avoid. Personally, I would avoid it here, simply because it's too wordy.
One more possibility, again trying to make the subjects parallel:
Not only should you cook your meals, but you should make them healthy.
Slight change in meaning, but works better.