Two-phase dendrites are needlelike crystals with a eutectic internal structure growing during solidification of ternary alloys. We present a scaling theory of these objects based on Ivantsov’s theory of dendritic growth and the Jackson-Hunt theory of eutectic growth. The additional introduction of the relationship ρ~λ (ρ: dendrite tip radius; λ: eutectic interphase spacing) suggested by recent experimental results [, Phys. Rev. Lett. 104, 056101 (2010)] leads to a complete solution of the selection problem and to the scaling rule ρ~v−1/2 (v: dendrite tip growth rate).