Measurements of the longitudinal and transverse spin relaxation times of holes in an ensemble of vertically tunnel-coupled self-assembled InAs/In0.53Al0.24Ga0.23As quantum dots (QDs), emitting in the telecom spectral range, are reported. The spin coherence is determined using the spin mode-locking method in the inhomogeneous ensemble of QDs. Modeling the signal allows us to extract the hole spin coherence time to be in the range of T-2 = 0.02 - 0.4 mu s. The longitudinal spin relaxation time T-1 = 0.5 mu s is measured using the spin inertia method. The parameters investigated allow us to suggest that the main relaxation mechanism at low magnetic fields is related to the electron-hole spin exchange.