The constraints from the measurements of the B -> X-s gamma decay rate on the parameter space of 3-Higgs Doublet Models (3HDMs), where all the doublets have nonzero vacuum expectation values, are studied at the next-to-leading order in QCD. In order to naturally avoid the presence of flavour changing neutral currents at the tree level, we impose two softly-broken discrete Z(2) symmetries. This gives rise to five independent types of 3HDMs that differ in their Yukawa couplings. We show that in all these 3HDMs (including the case of type-II-like Yukawa interactions) both masses of the two charged Higgs bosons mH(1)perpendicular to and mH(2)perpendicular to can be smaller than the top mass mt while complying with the constraints from B -> Xs gamma. As an interesting phenomenological consequence, the branching ratios of the charged Higgs bosons decay into the cb final states can be as large as 80% when their masses are taken to be below m(t) in two of the five 3HDMs (named as Type-Y and Type-Z). This light charged Higgs boson scenario provides a hallmark 3HDM signature that cannot be realised in Z(2) symmetric 2-Higgs doublet models. We find that in the Type-Y and Type-Z 3HDMs the scenario with 90 GeV < m(H1)+/-, m(H2)+/- < m(t) is ruled out by the direct searches at the LHC, but in the Type-Y 3HDM 80 GeV < m(H1)+/-, < 90 GeV and 90 GeV < m(H2)+/- < m(t) is allowed by B > X-s gamma and direct searches at LEP2, Tevatron and LHC due to the reduced sensitivity of these searches to the degenerate case m(H1)+ approximate to m(W)+ . The cases where only one or both charged Higgs bosons are above the top quark mass are also naturally allowed in the both Type-Y and Type-Z 3HDMs.