We propose a novel multi-stream framework for continuous conversational speech recognition which employs bidirectional Long Short-Term Memory (BLSTM) networks for phoneme prediction. The BLSTM architecture allows recurrent neural nets to model longrange context, which led to improved ASR performance when combined with conventional triphone modeling in a Tandem system. In this paper, we extend the principle of joint BLSTM and triphone modeling to a multi-stream system which uses MFCC features and BLSTM predictions as observations originating from two independent data streams. Using the COSINE database, we show that this technique prevails over a recently proposed single-stream Tandem system as well as over a conventional HMM recognizer.