Is it a good or bad (or indifferent) idea to mix mounding plants like mondo grass or liriope with something like Asian jasmine or blue star creeper in the same bed, such that the spreading plant fills in the spaces I want to leave between the mounding plants? I.e. companion planting the two types of ground cover?
There are issues with your suggestions; Trachelospermum asiaticum (Asian jasmine) is a large, twining plant, with a height and spread of 4-8 metres, and is not considered a ground cover plant, more usually being grown up a wall or support of some kind. Pratia pedunculata (blue star creeper) remains low to the ground at up to 10cm, with a spread of around 1.5 metres, but it does not like a lot of sun, preferring shade or partial shade; this obviously does not combine well with mondo grass which prefers full sun and, although a couple of varieties of Liriope will cope with shade, most also prefer full sun. Both mondo grass and Liriope will spread over time, so if you leave gaps, they will fill up with those two plants as time goes by anyway, though if the gaps are large, it will take some time for them to do so.
You mention ivy in your title; Hedera varieties grow well almost anywhere and are good in shady areas, but will spread far and wide (up, down and sideways) and can be difficult to control in terms of spread, so I would not recommend that mixed in with mounding ground cover plants.