It is expected that 5G/6G networks will exploit sub-6 GHz, millimetre wave (mmWave) and terahertz (THz) frequency bands simultaneously and will increase flexibility in user equipment (UE)-cell association. In this paper, we introduce a novel stochastic geometry-based framework for the analysis of the signal-to-interference-plus-noise-ratio (SINR) and rate coverage in a multi-tier hybrid sub-6GHz-mmWave-THz network, where each tier has a particular base station (BS) density, transmit power, bandwidth, number of BS antennas, and cell-association bias factor. The proposed framework incorporates the effects of sub-6 GHz, mmWave and THz channel characteristics, BS beamforming gain, and blockages. We investigate the downlink (DL) and uplink (UL) decoupled cell-association strategy and characterise the per-tier cell-association probability. Based on that, we analytically derive the SINR and rate coverage probabilities for both DL and UL transmissions. The analytical results are validated via extensive Monte Carlo simulations. Numerical results demonstrate the superiority of the DL and UL decoupled cell-association strategy in terms of SINR and rate coverage over its coupled counterpart.