Jennie Garth and Peter Facinelli
03/14/2012 at 08:00 PM EDT
The public announcement of their split
was painful enough, but Peter Facinelli and Jennie Garth
were blindsided – and deeply hurt – by the almost immediate flurry of Internet reports speculating infidelity had triggered the demise of their 11-year marriage.
So to set the record straight, the actors tell PEOPLE exclusively: "There are rumors out there which are completely untrue and hurtful to our family. We just want to make it very clear – there are no third parties involved."
The statement, made jointly by Facinelli, 38, and Garth, 39, comes a day after they jointly announced their plans to divorce
"While we have decided to end our marriage, we both share the same deep love and devotion to our children. We remain dedicated to raising our beautiful daughters together. We ask for privacy and respect during this time," they said Tuesday in a statement
The pair, who have three daughters
– Luca, 14, Lola, 9, and Fiona, 5 – met on the set of TV movie An Unfinished Affair
in 1996, and married in 2001.
Facinelli is known for his roles in the Twilight films
and on Nurse Jackie
, while Garth played Kelly Taylor on the iconic Beverly Hills, 90210