We characterize a 1.14 mu m ultrastable semiconductor laser system for precision spectroscopy of Tm inner-shell clock transition using a frequency comb. We stabilize both the repetition and the carrier-envelope offset frequencies of a commercial Ti : sapphire femtosecond laser to a passive hydrogen maser using a home-built f-2f interferometer. By measuring the absolute frequency of the 1.14 mu m laser stabilized to a high-finesse ULE cavity, we determine the zero-expansion temperature point of the cavity and the rate of linear drift of the the cavity resonance frequency due to "aging" of the ULE glass. We achieve less than 10 Hz frequency instability of the laser within 1,000 s after the linear drift compensation. We also measured the absolute frequency of the 1.14 mu m transition in Tm to be 262 954 938 269 213(30) Hz.