Time-frequency (TF) representation has found wide use in many challenging signal processing tasks including classification, interference rejection, and retrieval. Advances in TF analysis methods have led to the development of powerful techniques, which use non-negative matrix factorization (NMF) to adaptively decompose the TF data into TF basis components and coefficients. In this paper, standard NMF is modified for TF data, such that the improved TF bases can be used for signal classification applications with overlapping classes and data retrieval. The new method, called jointly learnt NMF (JLNMF) method, identifies both distinct and shared TF bases and is able to use the decomposed bases to successfully retrieve and separate the class-specific information from data. The paper provides the framework of the proposed JLNMF cost function and proposes a projected gradient framework to solve for limit point stationarity solutions. The developed algorithm has been applied to a synthetic data retrieval experiment and epileptic spikes in EEG signals of infantile spasms and discrimination of pathological voice disorder. The experimental results verified that JLNMF successfully identified the class-specific information, thus enhancing data separation performance.