Tish Cyrus and Dominic Purcell are battening down the hatches -- refusing to respond to man-stealing rumors involving Noah Cyrus -- but they're also not hiding from cameras.

The married couple was out for a stroll Friday in Toluca Lake, CA, keeping the vibe very casual ... Tish wore a grey hoodie, joggers and a trucker cap -- while the former "Prison Break" star opted for a navy tracksuit.

Tish and Dominic soaked up some fresh air with a pal ... perhaps attempting to clear their heads from the swirling drama that's come after a wild report this week.

If you missed it ... the story claims Tish swooped in and stole Dominic from her 24-year-old daughter Noah, following her split from Billy Ray Cyrus.

Tish reportedly began connecting with DP in his DMs while he was dating Noah -- and there was also a suggestion of possible overlap ... a period when he was dating both mom and daughter.

Noah hasn't addressed the whole saga ... and ditto for her mother and, dare we say it, stepdad.

In the wake of the report, the rumor is this is why Noah skipped Tish and Dominic's wedding last August.

We've known that Tish is estranged from Noah, but now it also appears her other daughter, Miley Cyrus, is feuding with dad Billy Ray.