Maity and Sherman (2006) considered the situation in two-sample testing for the difference in means when one variance is assumed to be known while the other variance is treated as unknown. This problem arises in many real life situations, for example, when one is interested in comparing a standard treatment with a new treatment in medical studies. The variance for the standard treatment is assumed to be known from historical data, and the variance for the new treatment is unknown. Following the argument in Satterthwaite (1941, 1946), Maity and Sherman (2006) obtained the confidence interval for the difference in means based on an approximate t-distribution. In this paper, a likelihood-based third order asymptotic method is introduced to obtain the confidence intervals for the difference in means. Simulations are used to show that the proposed method has better coverage property than Maity and Sherman's t-method, especially when the sample sizes are small.