Radio interferometry calibration and radio frequency interference (RFI) removal are usually done separately. Here we show that jointly modelling the antenna gains and RFI has significant benefits when the RFI follows precise trajectories, such as for satellites. One surprising benefit is improved calibration solutions, by leveraging the RFI signal itself. We present trajectory-based RFI subtraction and calibration (tabascal), a new algorithm that jointly models the RFI and calibration parameters in visibilities. We test tabascal on simulated MeerKAT calibration observations contaminated by satellite-based RFI. We obtain gain estimates that are both unbiased and up to an order of magnitude better constrained compared to uncontaminated data. When combined with an ad hoc RFI subtraction scheme, tabascal solutions can be further applied to an adjacent target observation: 5 min of calibration data results in an image with about a third the noise achieved when using flagging alone. The recovered flux distribution of RFI subtracted data was on par with uncontaminated data. In contrast, RFI flagging alone resulted in a higher detection threshold and consistent underestimation of source fluxes. For a mean RFI amplitude of 17 Jy, using RFI subtraction leads to less than 1 per cent loss of data compared to 75 per cent data loss from an ideal 3σ flagging algorithm, a very significant increase in data available for science analysis. Although we have examined the case of satellite RFI, tabascal should work for any RFI moving on parametrizable trajectories, relative to the phase centre, such as planes and/or objects fixed to the ground.