Ensuring the spatial equity of health service facilities (HSFs) is crucial for the well-being of residents. However, previous research has predominantly focused on the accessibility and equity of single-type facilities, neglecting the residents’ demand for diversified types of health services. This study proposes a multi-type, Gaussian-based, two-step floating catchment area method (MT-G2SFCA) to assess the comprehensive accessibility and equity of multi-type HSFs in different age groups in the Hedong District of Tianjin, with the Gini coefficient and the bivariate local Moran’s I. Furthermore, the key factors affecting the accessibility were explored through a geo-detector. The results indicate the following: (1) Neglecting the health benefits of facility type diversity can result in an underestimation of the accessibility and equity; (2) neglecting the differences in walking ability of the elderly can result in an overestimation of the accessibility and equity; and (3) the Pedestrian Route Directness is the key factor affecting the accessibility and equity in high-density urban areas, and especially that the facility density is the key factor for the elderly. This research emphasizes the impact of facility type diversity on the accessibility and equity of HSFs, which can offer more precise and holistic technical assistance and policy recommendations for optimizing the allocation of HSFs.