This work presents a two-dimensional (2-D) study of the modal spectrum of a single microstrip and a pair of coupled microstrip lines with an upper dielectric half-space. This 2-D study is postulated as the necessary step previous to the 3-D investigation of the potential applications of leaky-wave antennas radiating in an environment susceptible to be modeled by a dielectric half-space. Thus the nature and the possible transitions of the modal spectrum will be characterized for a wide range of values of the permittivity of the upper half-space ($varepsilon$u). From a physical rationale, the modal spectrum is expected to comprise only leaky modes for values of $varepsilon$u greater than the permittivity of the line substrate ($varepsilon$). This hypothesis is corroborated by the computed numerical results, which, for the case of the microstrip with an air gap, also show that the above assertion is satisfied even for values of $varepsilon$u less than $varepsilon$. Although the nature of the mathematical transition from bound to leaky modes could not be rigorously established, there has been always found a physical transition from each fundamental bound mode (BM) to a space-wave leaky mode (SPWLM). This type of direct physical transition from a fundamental BM to a SPWLM, which is not allowed in a frequency evolution, has been proved to be mathematically viable.