Fill a large pot with lightly salted water and bring to a rolling boil. Cook linguine in boiling water until cooked through but still firm to the bite, about 11 minutes; drain, reserving 2 tablespoons pasta water.

Melt butter with olive oil in a saucepan over medium-low heat; when mixture begins to bubble, add shallots and cook until softened. Stir milk, salmon, and cream cheese into shallots. Mix in reserved pasta water until incorporated.

Transfer salmon mixture to a large serving bowl. Add linguine; toss until evenly combined.