Located in the stratospheric layer of Earth's atmosphere, the high altitude platform station (HAPS) is a promising network infrastructure, which can bring significant advantages to sixth-generation (6G) and beyond wireless communications systems by forming vertical heterogeneous networks (vHetNets). However, if not dealt with properly, integrated networks suffer from a number of performance challenges compared to standalone networks. In harmonized integrated networks, where different tiers share the same frequency spectrum, interference is an important challenge to be addressed. This work focuses on an integrated HAPSterrestrial network, serving users in an overlapped urban geographic area, and formulates a fairness optimization problem, aiming to maximize the minimum spectral efficiency (SE) of the network. Due to the highly nonconvex nature of the formulated problem, we develop a fast converging iterative algorithm that designs the massive multiple-input multiple-output (mMIMO) beamforming weights and the user association scheme such that the propagated inter-and intra-tier interference is managed. Simulation results demonstrate the proposed algorithm's superiority over standalone terrestrial networks and baseline algorithms.