The phrase betwixt and between means not fully or properly either of two things, in an intermediate or middling position; as an adjective, it means middling, indifferent, so-so. (The word betwixt is now mainly confined to this phrase.)
The sense of this phrase is similar to that of neither fish nor fowl.
The earliest quotation in the Oxford English Dictionary (2nd edition – 1989) dates from 1832, but I have found an occurrence in The Dublin Evening Post of 30th August 1781; I have not discovered to which member of the British government this ironic paragraph refers nor what “P—me S——” stands for (the position of Prime Secretary does not seem to have existed):
It is a matter of curious speculation with many, in what stile [= style] a quondam P—me S——, who, it is confidently said, is again come round to Government, will deliver his first speech from the Treasury-Bench. It is imagined Administration will consent for a few weeks, that he shall speak betwixt and between; and to divide on immaterial questions against them.—But if the conduct be left to the gentleman’s own choice, it is thought he would wish to wear a mask for the first month.
Another early instance of the phrase is from The Morning Chronicle (London) of 30th July 1810 (Cheltenham, in Gloucestershire (western England), became a fashionable spa town in the 19th century):
Cheltenham, July 26.
The company here (as at Bath and Brighton) is of such a mingled complexion, that the Master of the Ceremonies must be frequently embarrassed in ascertaining the social genus to which they may legitimately belong: many of them are neither Gentry are [misprint for nor] Plebeians, but, like the bat, something betwixt and between.—Mr. King (who is certainly the best arbiter of local elegance that hath been in a governing capacity since the days of Beau Nash) hath, it is said, divided this pyebald [= piebald] assemblage of dancing bipeds into different classes, which are arranged under the common designation of Hunters, viz.
Fortune Hunters! Wife Hunters! Husband Hunters! Dinner Hunters! Bottle Hunters! Legacy Hunters! Heir Hunters! Spinster Hunters! Booby Hunters! Title Hunters! and a few Health Hunters!