Muilenburg, James. "Chapter Six: Jewish Character." The Literary Relations of the Epistle of Barnabas and the Teaching of the Twelve Apostles. Marburg, 1929, 98-108.
Muilenburg finds in Barnabas strong statements against the 'old covenant' of the Jews, along with his apparent understanding of the intricacies ofJewish customs, a strong suggestion that the author is a recent convert to Christianity from Judaism (Muilenburg 1929, 98). Some of the cultural markers suggest the author is more familiar with Judaism as practiced in Alexandria than in Palestine (Muilenburg 1929, 99).
The Didache may well be compared to Barnabas as having a particular Jewish character. Muilenburg compares it to "a Talmud, probably the kind of manual or handbook employed by Jewish missionaries among proselytes" (Muilenburg 1929, 102). The Two Ways material is certainly rooted in Old Testament teaching. Muilenburg goes farther, by tracking down likely Jewish parallels for numerous ideas from Didache 7-15 (Muilenburg 1929, 105ff). This signals to me the level of continuity between Judaism and Christianity, where Christianity may be seen as a fulfillment of, rather than a sharp departure from, Judaism.