Yes, you are eligible to healthcare in Norway if you obtain a Family Visa (Residence Permit for Family Reunification). You will be allocated a fastlege (akin to a family doctor or general practitioner) with whom you must consult if you have any medical issues.
You just have to pay up to $260 per year for medical services (like a deductible). After receiving medical treatment up to this amount, you will receive an exemption card and will be eligible for free healthcare for the rest of the year.