With jpegs in emails (or on websites), there always needs to be a balance between quality and download size. (I’m not sure what you’re referring to when you mention their database opening files.)
In Photoshop, the export function makes it possible to see what any given image will look like with varying degrees of compression, which enables the designer to choose the most appropriate compromise.
There are other ways to deal with the problem, though, like making the photo a background image in a div, then positioning the type over it as a separate PNG file with a transparent background. The trouble with this approach is that not every email client will correctly display it.
There’s also the issue of what email service you might be using and what it might or might not be doing to your images behind the scenes.
With HTML email design the best approach is to recognize that HTML email and the email clients impose very severe limitations on what’s doable, then design the emails to make the best of what works and what won’t work as well. In other words, the best solution just might be to not place type over your images, even if it involves explaining to those who asked you to do it what the results will be.