The adsorption of the acid gas H2S has been explored in both MIL-47(V) and MIL-53(Cr) porous metal organic frameworks (MOFs) by combining infrared measurements and molecular simulations. It is shown that while the MIL-47(V) structure remains rigid upon H2S adsorption up to a pressure of 1.8 MPa, the MIL-53(Cr) solid initially present in the large pore form (LP) switches to its narrow pore version (NP) at very low pressure before undergoing a second structural transition from the NP to the LP versions at higher pressure. Such structural transitions further explain the different shape of the adsorption isotherms for both MILs. A further step consists of providing some insights into the microscopic arrangements of the adsorbate molecules within the pores of the MILs. At the initial stage of adsorption, the H2S molecules mainly form hydrogen bonded species, either as hydrogen donor (in MIL-47 V) or hydrogen-acceptor (in MIL-53Cr) with the mu(2)-O and mu(2)-OH groups, respectively, present at the MOF surfaces. At higher pressure (1.8 MPa), the adsorbates are preferentially arranged within the channel in order to form dimers with a high orientational disorder. Both experimental and simulated adsorption enthalpies for H2S decrease in the following sequence: MIL-53(Cr) NP > MIL-47(V) > MIL-53(Cr) LP. The conclusions drawn from this work are then discussed considering the use of such materials for the CH4/H2S separation by means of Pressure Swing Adsorption.