。
I woke up after midnight.
Literal
Midnight passed [at-に] woke-up-[polite past-ました].
夜中 ('midnight, middle of night') combines with the verb 過ぎる ('pass, exceed') to form 夜中過ぎ ('past midnight'). This is the noun form — 過ぎ as a suffix attaches to time expressions: 5時過ぎ ('past 5'), 昼過ぎ ('past noon'). 起きる here means 'wake up,' not 'get up' (both senses exist).