The profile Hidden Markov model (HMM) is a statistical model of a multiple sequence alignment (MSA). Profile HMMs are used in detecting sequence membership of protein families, protein structure prediction, and sequence alignment. However, on evolutionarily divergent datasets, the accuracy of alignments produced using profile HMMs degrade. We present a new statistical model for representing an MSA using multiple HMMs, which we call the Family of HMMs (fHMM). We show that using many HMMs instead of a single HMM to represent an MSA produces better alignment accuracy for sequence datasets with high evolutionary diameter. We present TIPP, a new method for taxonomic identification and profiling, that uses the fHMM model. We show that TIPP results in better classification accuracy (especially of novel reads) and more accurate abundance profiling. Furthermore, TIPP is more robust to sequencing errors, especially those resulting from indels, than other profiling methods.