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The road extraction task is mainly composed of two subtasks, namely, road detection and road centerline extraction. As the road detection task and road centerline extraction task are strongly correlated, in this paper, we introduce a multitask learning framework to detect roads and extract road centerlines simultaneously. For the road centerline extraction problem, existing works rely either on regression-based methods, or classification-based methods. The regression-based methods suffer from slow convergence and unsatisfactory local solutions. The classification-based methods ignore the fact that the closer the pixel is to the centerline, the higher our tolerance for its misclassification. To overcome these problems, we first convert the road centerline extraction problem into the problem of discrete normalized distance label prediction, which can be resolved by training an ordinal regressor. For the road extraction task, most of the previous studies apply pixel-wise loss function, for example, Cross-Entropy loss, which is not sufficient, as the road has special topology characteristics such as connectivity. Therefore, we propose a road-topology loss function to improve the connectivity and completeness of the extracted road. The road-topology loss function has two key characteristics: (i) The road-topology loss function combines road detection prediction and road centerline extraction prediction to promote the two subtasks to each other by using the correlation between the two subtasks; (ii) The road-topology loss can emphatically penalize gaps that often appear in road detection results and spurious segments that easily appear in centerline extraction results. In this paper, we select the AdamW optimizer to minimize the road-topology loss. Since there is no public dataset, we build a road extraction dataset to evaluate our method. State-of-the-art semantic segmentation networks (LinkNet34, DLinkNet34, DeeplabV3plus) are used as baseline methods to compare with two kinds of method. The first kind of method modifies the baseline method by adding the road centerline extraction task branch based on ordinal regression. The second kind of method uses the road topology loss and has the same network architecture as the first kind of method. For the road detection task, the two kinds of methods improve the baseline methods by up to $3.51\%$ and $11.98\%$ in $IoU$ metric on our test dataset, respectively. For the road centerline extraction task, the two kinds of methods improve the baseline methods by up to $8.22\%$ and $10.9\%$ in the Quality metric on our test dataset. Full article