The performance of a speaker verification system is severely degraded by spoofing attacks generated from artificial speech synthesizers. Recently, several approaches have been proposed for classifying natural and synthetic speech (spoof detection) which can be used in conjunction with a speaker verification system. In this paper, we attempt to develop a joint modelling approach which can detect the presence of spoofing attacks while also performing the speaker verification task. We propose a factor modelling approach where the spoof variability subspace and the speaker variability subspace are jointly trained. The lower dimensional projections in these subspaces are used for speaker verification as well as spoof detection tasks. We also investigate the benefits of linear discriminant analysis (LDA), widely used in speaker recognition, for the spoof detection task. Several experiments are performed using the speaker and spoofing (SAS) database. For speaker verification, we compare the performance of the proposed method with a baseline method of fusing a conventional speaker verification system and a spoof detection system. In these experiments, the proposed approach provides substantial improvements for spoof detection (relative improvements of 20% in EER over the baseline) as well as speaker verification under spoofing conditions (relative improvements of 40% in EER over the baseline).