There are too many variables to give a definite answer. It primarily depends on the pressure, temperature and the proportion of carbon dioxide. At 20 degrees C and 100 atmospheres pressure both carbon dioxide and water should be liquids.
Although some carbon dioxide would dissolve in the water this would be limited and two phases should be present providing your “salad dressing” ocean (all other things being equal).
At this temperature and pressure liquid carbon dioxide has a density of 856 kg/cubic metre so the carbon dioxide should float above the water.
Using this calculator https://www.peacesoftware.de/einigewerte/calc_co2.php7
it appears that at temperatures where carbon dioxide and water are both liquids that carbon dioxide would always be the upper phase as carbon dioxide is only heavier than water below zero where pure water would generally have already frozen.
That said all other things are unlikely to be equal. There are all sorts of complicating factors:
Interaction with rocks and other materials in the ocean are likely to introduce significant impurities such as dissolved salts. If these are present in high concentration then it is possible that the water phase might still be liquid at -15 degrees C. At this temperature carbon dioxide is actually heavier than pure water. And although probably not heavier than cold salt water, the difference might be small enough to allow convection and other effects* to create a suspension of the two phase to some extent.
Freezing could also be interesting. If the temperature decreased sufficiently to freeze the top of the water layer, it might become less dense than the carbon dioxide layer above and float up through it to the ocean surface.
*Mixing to form suspensions of one phase in another are bound to occur to some extent caused by currents, tides, weather, rain, winds, seasonal temperature variation and the surfactant action of impurities etc.