Sumatra PDF is a PDF, ePub, MOBI, CHM, XPS, DjVu, CBZ, CBR reader for Windows

Italics aren't show in epubs that are formatted correctly

[EDIT: Actually, it works just fine with mobi files so I’ll just use those instead. As you were.]

SumatraPDF ebook engine emulates older readers that had a single font (you can try any 1 windows font with a wider range of glyphs) most have Upright Bold and Italic styles. That approach works well for many older/simpler ebook formats but ePub is the newest kid on the block and thus more demanding of multiple / using more exotic internal styles.

Switching to use MuPDF internally for any of those formats it supports such as ePub would improve that feature, but it’s a question of programmer time to make such a significant change.