We present a new bandwidth extension algorithm for convert-ing narrowband telephone speech into wideband speech using a transformation in the mel cepstral domain. Unlike previous ap-proaches, the proposed method is designed specifically for band-width extension of narrowband speech that has been corrupted by environmental noise. We show that by exploiting previous re-search in mel cepstrum feature enhancement, we can create a uni-fied probabilistic framework under which the feature denoising and bandwidth extension processes are tightly integrated using a single shared statistical model. By doing so, we are able to both denoise the observed narrowband speech and robustly extend its bandwidth in a jointly optimal manner. A series of experiments on clean and noise-corrupted narrowband speech is performed to validate our approach.