In this paper, we describe the first generic construction for biometric Identity Based Encryption (IBE) considering two distance measures at the same time. Current protocols for fuzzy/biometric IBE consider either set overlap metric or Euclidean distance. However, the similarity measures for biometric templates can be quite different from those considered in theoretical works. For instance, a fingerprint template usually consists of a set of minutiae, and two templates are considered as similar if more than a certain number of minutiae in one template are near distinct minutiae in the other. In this case, the similarity measure has to consider both Euclidean distance and set difference at the same time. To achieve this property, our generic construction is based on two different biometric IBE systems encoding the same message. Specifically, we combine a fuzzy IBE-type scheme and the recently introduced Distance Based Encryption (DBE) scheme with minimum overhead in terms of public parameters, ciphertext and private key size. Also, we describe an efficient biometric IBE scheme denoted as ordFIBE, which is restricted for biometrics that can be represented as an ordered/grouped set of features. Finally, we instantiate the new construction based on ordFIBE and DBE of [1], which share the same setup phase, in particular, common public parameters.