A heating and hot-water supply apparatus includes a combustion means, a heat exchanger, a circulation passage, a circulation means, a bypass passage, a distribution means, a hot-water supply heat exchanger, a water entry passage, a hot-water supply passage, and a control means. The circulation passage connects an external heating terminal and the heat exchanger. The water entry passage supplies water of an external hot-water supply pipe and an external water supply pipe to the hot-water supply heat exchanger. The control means controls the distribution means to be adaptable to each of a heating operation and a hot-water supply operation. The control means prioritizes the hot-water supply operation when there is a hot-water supply request for warm water use in addition to a heating request, and prioritizes the heating operation when there is a temperature-maintaining request for maintaining a temperature of the hot-water supply pipe in addition to the heating request.