Begin by washing your canning jars, metal bands, and lids in hot soapy water. To sterilize, place jars in a stockpot filled with water and bring to a gentle simmer over medium heat. Allow the jars to warm for about 10 minutes.

Carefully wash the blackberries in cool water and let them drain. Blanch the peaches for 1 minute in boiling water, then plunge them into an ice bath to halt cooking. Once cool, peel and chop the peaches.

In a large saucepan, combine the blackberries, diced peaches, lemon juice, sugar, cinnamon, allspice, and nutmeg. Stir over low heat until the sugar dissolves, about 5 minutes.

Bring the mixture to a vigorous boil over medium-high heat. Add pectin and stir continuously for 1 minute until a rolling boil is reached.

Remove the jam from heat and fill each jar with the hot fruit mixture, leaving approximately 1/4 inch of headspace. Clean the rims of the jars and seal with lids and bands.

Submerge the filled jars in simmering water, ensuring they are covered by at least 1 inch of water. Process the jars for 10 minutes.

Carefully remove the jars and let them cool completely at room temperature for several hours or overnight.