With the rapid development of online recruitment platforms, a variety of emerging recommendation services have been witnessed for benefiting both job seekers and recruiters. While many researchers have studied the problem of reciprocal recommendation in two- sided markets (e.g., marriage market and real estate market), there is still a lack of in-depth understanding of the bilateral occupational preferences of different participants in the online recruitment market. To this end, in this paper, we propose a Bilateral Occupational-Suitability-aware recommender System (BOSS) for online recruitment, in consideration of the reciprocal, bilateral, and sequential properties of realistic recruitment scenarios simultaneously. To be specific, in BOSS, we first propose a multi-group-based mixture-of-experts (MoE) module to independently learn the preference representations of job seekers and recruiters. Then, with a specially-designed multi-task learning module, BOSS can progressively model the action sequence of recruitment process through a bilateral probabilistic manner. As a result, the reciprocal recommendations can be efficiently implemented by leveraging the product of different action probabilities of job seekers and recruiters. Finally, we have conducted extensive experiments on 5 real-world large-scale datasets as well as the online environment. Both online A/B test and offline experimental results clearly validate that our recommender system BOSS can outperform other state-of-the-art baselines with a significant margin.