Forensic DNA profiling is acknowledged as the model for a scientifically defensible approach in forensic identification science, as it meets the most stringent court admissibility requirements demanding transparency in scientific evaluation of evidence and testability of systems and protocols. In this paper, we propose a unified approach to forensic speaker recognition (FSR) oriented to fulfil these admissibility requirements within a framework which is transparent, testable, and understandable, both for scientists and fact-finders. We show how the evaluation of DNA evidence, which is based on a probabilistic similarity-typicality metric in the form of likelihood ratios (LR), can also be generalized to continuous LR estimation, thus providing a common framework for phonetic-linguistic methods and automatic systems. We highlight the importance of calibration, and we exemplify with LRs from diphthongal F-pattern, and LRs in NIST-SRE06 tasks. The application of the proposed approach in daily casework remains a sensitive issue, and special caution is enjoined. Our objective is to show how traditional and automatic FSR methodologies can be transparent and testable, but simultaneously remain conscious of the present limitations. We conclude with a discussion on the combined use of traditional and automatic approaches and current challenges for the admissibility of speech evidence.