May a wife be treated, or give birth, with a male doctor?

A female doctor is preferred if available and of equal expertise; if not, or in an emergency, treatment by a male doctor is permitted out of necessity and need, uncovering the aurat only as much as required.
A principle of fiqh holds that need can make permissible what is originally forbidden, based on Allah not wishing hardship (al-Baqarah 2:185) and the prohibition on harming oneself (al-Baqarah 2:195). Women Companions also treated wounded men in battle alongside the Prophet ﷺ. Practical steps: ask for a female doctor or nurse where possible; ask for a female nurse or the husband to be present during examinations; and do not delay necessary treatment simply because no female doctor is available. A husband should not prevent his wife from getting life-saving treatment on these grounds. See Modesty & boundaries.