Semi-seriously, connected (orientable) double covers of Möbius strips? (Requires two strips of each colour per model.)
Glue or tape a red strip to a white strip, making a single double-thickness strip that is red on one side and white on the other. (Optionally colour the white side to look like a fruit rind, such as watermelon.)
Make a second unit of the same type.
Place two of these units with red sides facing, making a single quadruple-thickness strip that is white on the outside and red on the inside as if the paper has been cut in half "depthwise."
Treating this quadruple-strip as a unit, create a Möbius strip conventionally: Give a half-twist, and "attach the ends, respecting the laminar division."
Tell math-y people you made a Möbius strip, cut the thickness of the paper in half, and this is what resulted!
As for semi-serious: The model clearly has two sides (one of each colour), and nicely illustrates how "orientable double-covering" amounts to "painting a non-orientable surface and peeling off the paint," i.e., picking a germ of orientation and constructing its connected component in the sheaf of local orientations.