What type of clothing is required when working around asbestos?
Check out this PDF from the Australian government (assuming the +61 in your profile means OZ)

Pages 29 and 30 deal with personal protective equipment. (PDF pages 42-43 AND WHY CAN"T ANY MAKE PDF page numbers work!!!)

Asbestos Removal Guidlines

I'll highlight this line:  The laundering of contaminated protective clothing in workers’ homes is strictly prohibited. 

Generally though, this is a workplace safety issue, and I'd contact the Ministry of Labour.