We study perturbations of functions f(A, B)of noncommuting self-adjoint operators Aand Bthat can be defined in terms of double operator integrals. We prove that if fbelongs to the Besov class B¹_∞,1(ℝ²), then we have the following Lipschitz-type estimate in the Schatten-von Neumann norm S_p, 1 ≤ p ≤ 2: ∥f(A₁, B₁) -f(A₂, B₁)∥S_p ≤ const(∥A₁-A₂∥S_p+∥B₁-B₂∥S_p). However, the condition f ε B¹_∞,1(ℝ²)does not imply the Lipschitz-type estimate in S_p with p < 2. The main tool is Schatten-von Neumann norm estimates for triple operator integrals.