Interface theories are employed in the component-based design of concurrent systems. They often emerge as combinations of Interface Automata (IA) and Modal Transition Systems (MTS), e.g., Nyman et al.'s IOMTS, Bauer et al.'s MIO, Raclet et al.'s MI or our MIA. In this paper, we generalise MI to interfaces, for which we properly resolve the longstanding conflict between unspecified inputs being allowed in IA but forbidden in MTS. With this solution we achieve, in contrast to related work, an associative parallel composition, a compositional preorder, a conjunction on interfaces with dissimilar alphabets supporting perspective-based specifications, and a quotienting operator for decomposing nondeterministic specifications in a single theory. In addition, we define a hiding and a restriction operator, complement conjunction with a disjunction operator and illustrate our interface theory by means of a simple example.