We perform a global statistical analysis of the two-Higgs-doublet model with generic sources of flavour violation using GAMBIT. This is particularly interesting in light of deviations from the Standard Model predictions observed in b→cτν¯ and b → sℓ⁺ℓ⁻ transitions as well as the indications for a charged Higgs with a mass of 130 GeV in top quark decays. Including all relevant constraints from precision, flavour and collider observables, we find that it is possible to simultaneously explain both the charged and neutral current B anomalies. We study the impact of using different values for the W mass and the Standard Model prediction for the anomalous magnetic moment of the muon and provide predictions for observables that can probe our model in the future such as lepton flavour violation searches at Belle II and Higgs coupling strength measurements at the high-luminosity LHC.