In a large saucepan, combine the apples, blackberries, sugar and lemon juice. Stir to combine.
Bring the mixture to a boil over medium-high heat, stirring occasionally. Reduce the heat to low and simmer for 15 minutes, stirring occasionally.
Add the thyme leaves and continue to simmer for an additional 10 minutes or until the mixture has thickened and is jam-like in consistency.
Remove from heat and let cool slightly before transferring to a jar or container with a lid. Store in the refrigerator for up to 2 weeks or freeze for up to 3 months.