We present an NLO simulation of WWbb production with massive b-quarks at the LHC. Off-shell and non-resonant contributions associated with top-pair and single-top channels and with leptonic W-boson decays are consistently taken into account using the complex-mass scheme. Thanks to the finite b-quark mass, WWbb predictions can be extended to the whole b-quark phase space, thereby including Wt-channel single-top contributions that originate from collinear g bb splittings in the four-flavour scheme. This provides a consistent NLO description of tt and Wt production and decay, including quantum interference effects. The simulation is also applicable to exclusive 0- and 1-jet bins, which is of great importance for Higgs-boson studies in the H WW channel and for any other analysis with large top backgrounds and jet vetoes or jet bins.