I think its the plastic (BPA) leaking into the formula, rather than the soap soaking into the plastic. If I remember correctly, the plastic gives off/releases it chemicals (BPA) when it is heated. So throwing the bottles into the dishwasher, is probably just releasing more of the plastic chemicals. If you are really concerned, I would switch to BPA-free plastic bottles, or I believe Dr. Brown's makes glass bottles. Definitely no worry about plastic there. But I know that is an expensive alternative to replace your entire bottle collection.
If your hubby is worried about the soap you are using to clean the bottles, maybe try switching to an organic or all natural brand. That way even if the soap is being absorbed into the plastic or leaving any kind of a residue, it would be "healthier" than regular store brand which probably has a lot of chemicals and dyes added in.
Good luck.