Is it unhealthy to stay awake during night time (up to 3am), despite sleeping enough during the day (8 hours - 3am to 11 am)?

Probably not: The time of the hours which you sleep are generally less important than the number of hours. Though you can throw off your circadian rhythm (natural day-night cycle), it doesn't harm most. Some, however, can develop signs/symptoms of sleep disorders like insomnia. It has also been associated with others: obesity, diabetes, sad, etc. See your pcp if you have health issues.