Drain cherries, reserving juice. Pat cherries dry. Finely chop cherries, measure 1/3 cup. Spread cherries on paper towels; pat dry.
In a large bowl, combine butter and cream cheese. Beat with an electric mixer on medium to high speed for 30 seconds. Add sugar and salt. Beat until combined, scraping bowl occasionally. Beat in egg and almond extract until combined. Gradually add flour, beating until combined.
Divide dough into 3 portions. Leave one portion plain. Into another dough portion, knead 1/2 teaspoon of the reserved cherry juice and enough red food coloring to make dough light pink. Knead chopped cherries into remaining dough portion. Wrap each dough portion in plastic wrap. Chill for 2 hours or until easy to handle.
Lightly flour 3 pieces of parchment paper. On each piece, roll a dough portion into a 6-inch square. Cover each dough square with plastic wrap and freeze for about 30 minutes or until firm.
Place plain dough square on work surface; brush top with milk. Place pink square on top of plain square; brush pink square with milk. Top pink square with cherry square. Evenly trim edges of dough stack, lightly pressing layers together. Cut dough stack into thirds. Cover each portion; freeze for about 20 minutes or until firm.
Preheat oven to 375. Line cookie sheets with parchment paper. Cut each block crosswise into 12 slices. Place slices on prepared cookie sheets. Lightly press together any layers that separate.
Bake in the preheated oven for about 10 minutes, or until edges are light brown. Transfer to a wire rack; cool.
TO STORE: layer cookies between sheets of waxed paper in an airtight container; cover. Store at room temp for up to 3 days, or freeze for up to 3 months. (thaw cookies at room temperature.)