In this paper, we propose a novel end-to-end framework for training a spoof-aware speaker verification (SASV) system. To match the SASV scenario, where the test samples may be either spoof or genuine, we propose a novel contrastive objective and a modified mixup regularization strategy. The proposed end-to-end system and other SASV systems were evaluated on the ASVSpoof2019 LA evaluation set according to the SASV 2022 challenge rules. Our results showed that the proposed framework can learn complementary information to the conventional embedding fusion-based SASV systems. Using the proposed system in conjunction with the conventional embedding fusion systems has achieved a relative improvement of 61.07% in terms of SASV-EER compared to the best performing baseline result provided by the challenge organizers.