As @AtmosphericPrisonEscape noted in comments, above, "Extrasolar" is the correct term. E.g., we refer to "extrasolar planets", not "interstellar planets."
"Interstellar" refers to things among the stars (Merriam-Webster: "located, taking place, or traveling among the stars especially of the Milky Way galaxy")
"Extrasolar" means "outside the Solar System." (Merriam-Webster: "originating or existing outside the solar system")
One distinction is that "interstellar" doesn't include all space outside the Solar System -- "Interstellar space" is usually spoken of as distinct from, and much smaller than, "Intergalactic space".
The original question asked for "a general adjective for objects outside our solar system" and that would be "extrasolar".