PORTLAND, Maine — A brother and sister are appealing their murder convictions for killing the woman’s husband in his Old Orchard Beach home and trying to make it look like he was the victim of a home invasion.

Jeffrey Williams of West Hempstead, N.Y., is serving a life sentence and his sister, Darlene George, is serving 40 years after the two were tried together in the 2008 death of George’s husband, Winston George.

The Maine Supreme Judicial Court is hearing their appeals on Thursday.

Among other things, Williams and Darlene George are arguing that they should have had separate trials.

Police said Winston George was strangled with a rope and suffocated with a plastic bag, and that an empty rum bottle was stuffed into his mouth.