The couple's four-year-old younger daughter escaped the assailants by fleeing from home.
One person has been detained in connection with the incident, said Darjeeling's Superintendent of Police Akhilesh Chaturvedi
Kalimpong Additional Superintendent of Police Anjali Singh said the husband Dominik Bhutia worked with a cable operator.
Locals saw the victims lying in a pool of blood in their house Thursday morning and informed police. The bodies have been sent for post mortem.
Chaturvedi said the Tibetan couple had converted to Christianity. He hoped the case would be solved soon.
Himalayan Buddhist Association general secretary and Tibetan Support Group's north east India core committee convenor Sonam Londrup Lama has condemned the incident and demaned exemplary punishment of the culprits.
Various other organisations in Kalimpong have also raised their voice against the attack.