Transmittance of glass

In fact it depends on the type of glass. Depicted is solar transmittance through glas. For greenhouses special heat absorbing glas may be used. The diagram shows a dip of transmittance at $\approx 1200\,$nm. Lower transmittance is because absorption (see heat aborbing glass in diagram) and as well in reflection (see Fresnel equations). Your reasoning is right: the glas of a greenhouse may reflect infrared light.

The most common types have a transmission band up to the NIR (near infrared) regime. E.g. crown glas ($350\,\text{nm}<\lambda <2\,\mu$m) and fused silica ($200\,\text{nm}<\lambda <3\,\mu$m).